A is a 3 x 3 matrix with Three pivot positions aDoes the equ

A is a 3 x 3 matrix with Three pivot positions.

(a)Does the equation Ax = 0 have a nontrivial solution?

(B)Does the equation Ax = b have at least one solution for every possible b?

When A is a 3*3 matrix with Two pivot positions.

(a) Does the equation Ax = 0 have a nontrivial solution?

(B)Does the equation Ax = b have at least one solution for every possible b?

A is a 3 x 3 matrix with Three pivot positions. -

if a n*n matrix has n pivots , it means it has unique solution.

Ax = 0 , then only solution is 0 , that is trivial ,

if Ax = b, for b not equal to 0, then we get non-trivial solution for each different value of b.SO,

(a)Does the equation Ax = 0 have a nontrivial solution?

false

(B)Does the equation Ax = b have at least one solution for every possible b?

TRUE

When A is a 3*3 matrix with Two pivot positions.

if n*n matrix has less than n pivot positions,

then

Ax =0 has infinitely many solution.

Ax = b can have 0 or infinite solutions

(a) Does the equation Ax = 0 have a nontrivial solution?

true

(B)Does the equation Ax = b have at least one solution for every possible b?

False